
analogueCheck = () -> (
     
     R=QQ[a,b,c,e,f,m,k, x,y,z,t, Degrees=>{0,0,0,0,0,0,0,1,1,1,1}]; -- Ring of homogeneous coordinates.
     
     quintic=(x+m*y+a*z)^2*t^3+(a^2*x^3+x*y*(b*x+c*y)+m^2*y^3+(e*x^2+f*x*y+c*y^2)*z+(b*x+e*y)*z^2+z^3)*t^2+(2*a*x^3*y+e*x^2*y^2+2*a*m*x*y^3+(2*a*m*x^3+f*x^2*y+f*x*y^2+2*m*y^3)*z+(c*x^2+f*x*y+b*y^2)*z^2+2*(m*x+a*y)*z^3)*t+x^3*y^2+a^2*x^2*y^3+x*y*z*(2*m*x^2+b*x*y+2*a*y^2)+z^2*(m^2*x^3+c*x^2*y+e*x*y^2+y^3)+(m*x+a*y)^2*z^3;
     
     myquintic = sub(quintic, {t=>1, x=>x-m*y-a*z}); -- dehomogenize and make quadratic part square of linear term.

     q3 = part(3, sub(myquintic, x=>0));
     
     gamma = diff(z^3, q3)/6;

     g1 = diff(y^3,q3)/6;
     g2 = diff(z*y^2,q3)/2;     
     g3 = diff(y*z^2,q3)/2;
       
     blowup = sub(sub(myquintic,{x=>x*y,z=>z*y})/y^2,R); -- Blowup in the direction of y.
       
     f2 = part(2,blowup); -- Quadratic part after the blowup.
     f3 = part(3,blowup); -- Cubic part after the blowup.
     
     g4 = -((diff(x*y,f2))^2 - (diff(x^2,f2))*(diff(y^2,f2)));
          
     mu = diff(x*y, f2)/2;
     
     ff2 = sub(f2, x => -mu*y);
     ff2 = ff2*4;
     
     ff3 = sub(f3, x => -mu*y);
     ff3 = ff3*4;
     
     gg5 = (-1)*(diff(y^3, ff3)/6);
     
     g5 = (gg5 + 3*g4*m*a^2 - g4*b)/4;
     
     g6 = diff(z*y^2,ff3)/4;
         
    )


